2011-12 Archive

2011-12 Archive

Autumn 2011Autumn 2011

Air flow over non-rigid surfaces: Stability and acoustics

Date: Monday 17th October, 2pm, S1.20Speaker: Ed Brambley (University of Cambridge)Abstract: Within aircraft engine intakes, acoustic duct linings are routinely installed to reduce engine noise. It would be rather embarrassing if these acoustic linings were to cause an unpredicted loss of engine efficiency. The simple mathematical model of an acoustic lining in a duct with uniform flow has been in use for over half a century to inform aircraft engine designs, and the same mathematical model governs the stability and acoustics of flow over any range of surfaces, from elastic membranes to resonators to thin shells to vortex sheets. However, this simple mathematical model is inherently flawed: it is ill-posed. In this talk, the reasons for this and the effects of this will be explained. What does it mean to be ill-posed, and why should we care? What well-posed models can we come up with, and how do these lead to different predictions? An finally, are acoustic linings in aircraft engines causing a previously unpredicted loss of engine efficiency?

Landau poles, quasi-modes, and the formation of structures on planar vortices

Date: Monday 24th October, 2pm, S3.05Speaker: Andrew Gilbert (University of Exeter)Abstract: The talk will review some work with Matthew Turner (Surrey) on the internal dynamics of smooth two-dimensional vortices. We will consider how disturbances to such vortices are governed by a `Landau pole', giving exponential decay which corresponds not to a normal mode of the linear equations, but to a so-called `quasi-mode'. We will discuss how these poles can be obtained numerically and how they give insight into thresholds for the formation of long-lived, inviscid cats' eyes and tripole structures.

Extracting superconvergence for discontinuous Galerkin solutions

Date: Monday 31st October , 2pm, S1.20Speaker: Jennifer Ryan (Delft University of Technology)Abstract: The discontinuous Galerkin method (DGM) has recently become one of the most widely researched and utilized discretization methodologies for solving problems in science and engineering. It is fundamentally based upon the mathematical framework of variational methods, and provides hope that computationally fast, efficient and robust methods can be constructed for solving real-world problems. By not requiring that the solution be continuous across element boundaries, DGM provides a flexibility that can be exploited both for geometric and solution adaptivity and for parallelization. This freedom comes at a cost. Lack of smoothness across elements can hamper simulation post-processing like feature extraction and visualization. Therefore the development of smoothness-increasing accuracy conserving (SIAC) filters that respect the mathematical properties of the data while providing levels of smoothness so that commonly used visualization tools can be used appropriately, accurately, and efficiently. The development of SIAC filters is through the exploitation of superconvergence. This means that instead of the usual k+1/2 order accuracy of DGM in the L2-norm, we can see 2k+1 order accuracy in this special negative-order norm, where k is the highest degree polynomial used in the approximation. The trick is to draw this information out of the approximation so that it can be useful mathematically and computationally. This 'hidden accuracy' can be extracted through the use of a special convolution kernel that is composed of a linear combination of B-splines. One drawback of the original method is that the proofs for the effectiveness of this method are for linear hyperbolic equations that rely on a periodic boundary conditions as well as translation invariance of the mesh. This talk will focus on overcoming these difficulties (equation types, post-processing near boundaries, and mesh structures). Furthermore, we will address how this technique can be exploited for improved visualization of streamlines.

In the blink of an eye — Tear dynamics

Date: Monday 7th November, 2pm, S1.20Speaker: Colin Please (University of Southampton)Abstract: The thin layer of tears that cover the eye are continually refreshed by blinking and this plays an important role in keeping the eye healthy. Mathematical models to help understand how the tears are deposited on the eye during a blink and how the thin film behaves will be explored. A simple fluid dynamics model exploiting lubrication theory for the flow during the opening of an eye will be described as well as some extensions to account for numerous physical mechanisms that attempt to control the thickness and stability of the tear layer. A mixture of numerical methods and asymptotic methods will be described for analysing the models. The possible implications for treatment of 'dry eye syndrome' will be outlined.

Two-dimensional turbulence and coherent vortex structures

Date: Monday 14th November, 2pm, S1.20Speaker: GertJan van Heijst (Eindhoven University of Technology)Abstract: In contrast to its counterpart in the 3D world, turbulence in 2D is characterized by an inverse energy cascade. The presence of this inverse cascade in 2D turbulence is visible in the so-called self-organization of such flows: larger coherent vortex structures are observed to emerge from initially random flow fields. The lecture will address the evolution of 2D turbulent flows on a finite domain with no-slip walls. The organized state consists of a large, domain-filling cell. Results of both laboratory experiments in rotating / stratified fluids and numerical simulations have revealed the crucial role played by the unsteady boundary layers: the domain boundaries act as important sources of large-amplitude vorticity filaments that may influence the motion in the interior. Attention will be given to global flow quantities like the kinetic energy, the enstrophy, and the total angular momentum. In the case of forced 2D turbulence, the latter quantity may show a remarkable flip-flopping behaviour, associated with a collapse of the organized flow state followed by its re-organization. Experiments have been performed in a shallow fluid layer, in which the flow was driven by electromagnetic forcing. High-accuracy PIV measurements have revealed that substantial 3D effects may be present in such flows, in contrast to what is commonly believed. Although phenomena as the inverse energy cascade are clearly observed, the laboratory experiments suggest that one should be cautious when claiming detailed properties of such flows under the assumption of them representing 2D turbulence.

The effect of rotation on internal solitary waves: the Korteweg-de Vries and wave packet paradigms

Date: Monday 21st November, 2pm, S1.20Speaker: Roger Grimshaw (Loughborough University)Abstract: In the weakly nonlinear long wave regime, solitary waves are often modelled by the Korteweg-de Vries equation, which is well-known to support an exact solitary wave solution. However, when the effect of background rotation is taken into account, the resulting relevant nonlinear wave equation, the Ostrovsky equation, does not support an exact solitary wave solution. Instead an initial solitary-like disturbance decays into radiating oscillatory waves. In this talk, we will demonstrate through a combination of theoretical analyses, numerical simulations and laboratory experiments that the long- time outcome of this radiation is a nonlinear wave packet, whose carrier wavenumber is determined by an extremum in the group velocity.

On the formation of multiple zonal jets in the oceans

Date: Monday 28th November, 2pm, S1.20Speaker: Pavel Berloff (Imperial College)Abstract: Multiple alternating zonal jets observed in the ocean are studied with an idealized model with imposed large-scale background flow. The jets are maintained by the mesoscale eddies with mixed barotropic-baroclinic dynamics. The eddies drive the jets by either Reynolds or form stresses, depending on the direction of the background flow. The underlying dynamical mechanism of the jet formation is illuminated with the linear stability analysis. The mechanism is non-local in space, and it involves interactions between the unstable and weakly stable linear modes. Also, by looking at the efficiency of eddy fluxes associated with the linear eigenmodes, we explain why relative strength of the jets is controlled by the bottom friction.

Nonlinear Waves in Granular Chains

Date: Monday 5th December, 2pm, S1.20Speaker: Mason Porter (University of Oxford)Abstract: I will discuss recent investigations of highly nonlinear solitary waves in granular chains using numerical computations, analytical calculations, and experiments. I will provide an introduction to granular chains, and then I will focus on the dynamics of intrinsic localized modes (aka, discrete breathers) in diatomic chains and chains with defects.

Physical mechanisms and simulations of sea rogue waves

Date: Monday 12th December, 2pm, S1.20Speaker: Alexey Slunyaev (Keele University)Abstract: Rogue (freak) waves in the ocean are now a part of marine natural hazards. They are among waves naturally observed by people on the sea surface that represent inseparable feature of the Ocean. Rogue waves appear from nowhere, cause danger and disappear at once. They may occur at the surface of a relatively calm sea, reach not very high amplitudes, but be fatal for ships and crew due to their unexpectedness and abnormal features. The serious studies of the phenomenon started about 20–30 years ago and have been intensified during the recent decade. The research is being conducted in different fields: in physics (search of physical mechanisms and adequate models of wave enhancement and statistics), in geoscience (determining the regions and weather conditions when rogue waves are most probable), and in ocean and coastal engineering (estimations of the wave loads on fixed and drifting floating structures). Thus, scientists and engineers specializing in different subject areas are involved in the solution of the problem. Two general issues of the problem will be addressed by the talk: physical mechanisms of rogue wave occurrence, and their simulations in numerical experiments. Nonlinear mechanisms will be most emphasized.

Spring 2012Spring 2012

The interaction of cavitation bubbles with density interfaces

Date: Monday 30th January, 2pm, S1.20Speaker: David Leppinen (University of Birmingham)Abstract: In this talk we will use the Boundary Integral Method to examine the dynamics of the interactions of cavitation bubbles with a density interface. We will assume that the flow is inviscid, incompressible and axisymmetric in order to isolate the affect of bubbles interacting with a density interface. We will consider both explosive bubbles and bubbles which are ultrasonically forced.

Aerodynamic Control of Wind Turbine Blades and Long-Span Bridges

Date: Monday 13th February, 2pm S1.20Speaker: Prof. Mike Graham (Imperial College)Abstract: Wind turbines (and also long-span suspension bridges) stand in the lower part of the Atmospheric Boundary Layer of the natural wind which is both highly turbulent and subject to significant mean shear. Both of these phenomena as well as wake impact from other rotors generate high levels of unsteady loading on horizontal axis wind turbine rotor blades. The unsteady loads together with cyclic gravitational loads largely determine the fatigue life of the blades. This is a major design driver with a strong influence on the ultimate cost of the energy produced. Similar effects with, in addition, the effects of incident waves, apply to tidal stream turbines. The talk will describe an investigation into the effectiveness of controlled trailing edge flaps in counteracting unsteady loads. The flaps may be of small chord ( < 5% blade chord) if rapid activation is desired and numerical simulation and laboratory experiments will be described which have shown that short flaps can achieve as much as an 80% reduction in the amplitude of unsteady loading using the blade section lift as the control input. The possibility of using variable flexibility of the blade section camber as an alternative to flaps will also be discussed. Long span bridges suffer from buffeting but in addition are subject to the increasing difficulty as spans become longer of keeping the bridge stiff enough in torsion and heave so that the critical flutter speed remains well above the maximum ‘once-in-fifty-year' gust speed. The use of controlled flaps, which because of the possibility of winds from either direction include leading edge flaps, can aid this problem by significantly raising flutter speeds as well as contributing a reduction in buffet loads.

Coupled Problem of Dam-Break Flow

Date: Monday 20th February, 3pm, S3.05Speaker: Alexander Korobkin (UEA)Abstract: The initial stage of the flow with a free surface generated by a vertical wall moving from a liquid of finite depth in a gravitational field is studied. The liquid is inviscid and incompressible, and its flow is irrotational. Initially the liquid is at rest. The wall starts to move from the liquid with a constant acceleration. It is shown that, if the acceleration of the plate is small, then the liquid free surface separates from the wall only along an exponentially small interval. The interval on the wall, along which the free surface instantly separates for moderate acceleration of the wall, is determined by using the condition that the displacements of liquid particles are finite. During the initial stage the original problem of hydrodynamics is reduced to a mixed boundary-value problem with respect to the velocity field with unknown in advance position of the separation point. The solution of this problem is derived in terms of complete elliptic integrals. The initial shape of the separated free surface is calculated and compared with that predicted by the small-time solution of the dam break problem. It is shown that the free surface at the separation point is orthogonal to the moving plate. Initial acceleration of a dam, which is suddenly released, is calculated.

Large Amplitude Internal Waves in Weakly Stratified Oceans

Date: Monday 27th February, 2pm, S1.20Speaker: Roxana Tiron (University College, Dublin)Abstract: We consider large amplitude internal waves in weakly stratified fluids and obtain the nonlinear evolution equations, which generalize the strongly nonlinear model for a system of two constant density layers. After the linear dispersion relation of the new model is compared with that of the linearized Euler equations, the solitary wave and conjugate state solutions of the model are obtained and compared with other theoretical solutions and field data.

Mathematical Modelling of Bacterial Biofilm Growth

Date: Monday 5th March, 3pm, S3.05Speaker: John Ward (Loughborough University)Abstract: In this talk I will be presenting some of my work, in collaboration with many others, on the growth and regulation of bacterial biofilms; these are slimy colonies of non-motile bacteria on solid-fluid surfaces that have a number of implications in medicine and industry. The models to be discussed consist of nonlinear systems of PDEs and were analysed using asymptotic and computational methods. The main results and insights drawn from the work will be summarised.

The Stability of Jets in Diesel Engines

Date: Monday 12th March, 3pm, S3.05Speaker: Matthew Turner (University of Surrey)Abstract: This talk focuses on the stability of jets, with particular focus to fuel jets in Diesel engines. CFD simulations of jet and spray penetrations in Diesel engines use the stability theory of jets to determine break-up times, and break-up lengths. However it is found that these current CFD approaches underestimate the break-up lengths by a large amount, so the effects of acceleration are believed to be important. This talk concentrates on steady jets to try to understand the fundamental stability processes in these jets, so this theory can then being applied to unsteady jets.

Global Modelling of Ocean Tides

Date: Monday 26th March, 3pm, S3.05Speaker: Stephen Griffiths (University of Leeds)Abstract: A longstanding challenge in oceanography is the production of accurate global maps of the amplitude and phase of the ocean tides, from simple hydrodynamical equations with appropriate astronomical forcing and global topography. Over the last forty years, such prognostic models have improved in accuracy, partly due to increases in computing power, but also as the role of supposedly secondary physical processes have been recognized. Here, the development of a new prognostic global tidal model is described, based upon the solution of large sparse matrix systems coupled with iterations to account for nonlinear processes. Special emphasis is placed upon the modelling of small-scale internal waves of tidal frequency, which modify the surface tides via an internal tide drag. Results from this modelling work will be illustrated through animations to emphasize the dynamical processes involved.

Summer 2012Summer 2012

The stability of the liquid lining in fluid-conveying curved tubes

Date: Monday 14th May, 2pm, S1.20Speaker: Matthias Heil (University of Manchester)Abstract: Motivated by an interest in the fluid mechanical behaviour of the liquid film that lines the pulmonary airways, we demonstrate that the surface-tension-driven migration of fluid towards the outer wall of a curved vessel can be opposed by the azimuthal shear stresses generated by the Dean-like secondary flows that develop when air is driven along the vessel. Assuming the pressure-driven flow along the curved vessel to be fully developed, we employ a combination of numerical and asymptotic approaches to demonstrate that the competition between the two effects allows the existence of steady solutions in which the liquid lining has finite thickness along the entire perimeter of the vessel. We study the stability of these steady solutions and contrast the predictions obtained from a thin-film model that allows a detailed analysis of the system's bifurcation structure to the results of full numerical simulations based on the free-surface Navier–Stokes equations.

Multiscale models of growth and transport in biological tissues

Date: Monday 21st May, 2pm, S1.20Speaker: Oliver Jensen (University of Nottingham)Abstract: In building mathematical models of biological tissues, it is often necessary to link phenomena operating at very disparate length scales. I will describe two applications, each with a biomechanical flavour, where we have used multiscale approaches to relate microscopic and macroscopic processes. The first is a growing plant root, where a hierarchy of models are needed to connect the action of hormones and enzymes on the walls of individual plant cells to the development of the whole organ. The second example is the human placenta, where maternal blood flows past a disordered array of fetal blood vessels; here we investigate the usefulness of homogenization approximations in stochastic domains.

Thermally and mechanically driven quantum turbulence in helium II

Date: Monday 28th May, 2pm, S1.20Speaker: Andrew Baggaley (Newcastle University)Abstract: Quantum turbulence can be generated in superfluid helium either thermally (by applying a heat flux, as in thermal counter-flow) or mechanically (by stirring the liquid). We model the superfluid vortex lines as reconnecting space curves with fixed circulation, and the driving normal fluid as a uniform flow (for thermal counter-flow) and a synthetic turbulent flow (for mechanically driven turbulence). We compare the two forms of turbulence by computing their energy spectrum, distribution of curvature and amount of reconnections. Finally, we propose a method to experimentally detect the presence of superfluid vortex bundles.